Problem 2 (determine the appropriate sample size for p-chart) A fraction nonconforming control chart is to be established with a center line of 0.01 and two-sigma control limits. (a) How large should the sample size be if the lower control limit is above zero

n > 396 or n≥ 397

Step-by-step explanation:

Given

Center line, p = 0.01

2 sigma control limit, L=2;

For a 2 sigma control limit, the size of the sample size if the lower control limit is > 0 is given as;

n > ((1-p)/p)L²

Substitute 2 for L and 0.01 for p in the above expression

n > ((1-p)/p)L² becomes

n > ((1-0.01)/0.01) * 2²

n > ((0.99/0.01)) * 2²

n > 99 * 2²

n > 99 * 4

n > 396

So, the sample size should be greater than 396 (at least 397).

We can represent it as

n > 396 or n≥ 397

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb